I couldn't help but do some preliminary research on William Brewster, elder of the Plymouth Colony, who is one of my distant ancestors. Of his children, Jonathan, Patience, Fear, Love, and Wrestling, several died of smallpox in the New World, and they brought some adopted charges, the More children, with them; there are a lot of stories in here. We are descended from Patience, through a number of daughters, down to a son or two, and through a daughter who married my great-great grandfather.
So unlike the Leveretts, the line of descent is clear. And unlike the Puritans, the Pilgrims were more like the Quakers - they simply dropped out of the Church of England and paid the price. The price was living in the Netherlands for many years and ultimately going to the New World.
I got most of my information here as Wikipedia seems to compile the generally known, generally uncontroversial details. From this page you go off and find where people argue one way or another, and point out interesting facts about the nature of the Pilgrim community. Much is written about the Mayflower, for example, as it had the distinction of being the first, so early, and I think if anybody wrote anything about it whatsoever, it very well may have already been dug up and examined many times.
Although William Brewster arrived on the Mayflower in 1620, Patience and Fear did not arrive until three years later. I was surprised to find out that Love was a boy, but he was. Plymouth Colony had as one of its major settlements a town called Duxbury, and we have other ancestors who started out there, which leads me to wonder about the different motivations of Puritans and Pilgrims, especially with regard to tolerance. The Pilgrims, having dropped out of the church altogether, had a general tolerance I believe that we don't see in Boston or parts up there.
But what about the personal aspects? Starting up a new life on the Plymouth peninsula would be a hard choice for Patience and Fear, both of whom were women, I believe.
The list of famous Americans who are descended from Elder Brewster is long; it includes Katherine Hepburn, Ted Danson, Julia Child, Bing Crosby, Howard Dean, George McClellan, Sarah Palin, Nelson Rockefeller and Adlai Stevenson. These are just the ones who stand out to me, but what it means is that, basically, when their name comes up, I can say that they are a distant relative. If we share Elder Brewster as a common ancestor (albeit fourteen generations up, or something like that), then they may even be cousins, like fourteenth cousin, etc. Not that I would want to claim each of them, but hey, that's true even of my first and second cousins.
There could be more in here than I suspect.